# Solve the Following Systems of Equations: X/7 + Y/3 = 5 X/2 - Y/9 = 6 - Mathematics

Solve the following systems of equations:

x/7 + y/3 = 5

x/2 - y/9 = 6

#### Solution

The given system of equation is

x/7 + y/3 = 5 ...(i)

x/2 - y/9 = 6.....(ii)

From (i), we get

=> (3x + 7y)/21 = 5

=> 3x + 7x = 105

=> 3x = 1.5 - 7y

=> x = (105 - 7y)/3

From (ii), we get

(9x - 2y)/18 = 6

=> 9x -  2y = 108......(iii)'

Substituting x = (105 - 7y)/3  in  (iii) we get

9(105 - 7y)/3 - 2u = 108

=> (948 - 63y)/3 - 2y = 108

=> 945 - 63y - 6y = 108 x 3

=> 945 - 69y = 324

=> 945 - 324 = 69y

=> 69y = 621

=> y = 621/69 = 9

Putting y = 9in x = (1105 - 7y)/3 we get

x = (105 - 7 xx 9)/3 = (105 - 63)/3

= x = 42/3 = 14

Hence, the solution of thee given system of equations is x = 14, y = 9

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method
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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.3 | Q 6 | Page 44